An overview of theory and practice on process capability indices for quality assurance

Process capability indices (PCIs), C_p, C_a, C_pk, C_pm, and C_pmk have been developed in certain manufacturing industry as capability measures based on various criteria, including process consistency, process departure from a target, process yield, and process loss. It is noted in certain recent quality assurance and capability analysis works that the three indices, C_pk, C_pm, and C_pmk provide the same lower bounds on the process yield. In this paper, we investigate the behavior of the actual process yield, in terms of the number of non-conformities (in ppm), for processes with fixed index values of C_pk=C_pm=C_pmk, possessing different degrees of process centering. We also extend Johnson's [1992. The relationship of C_pm to squared error loss. Journal of Quality Technology 24, 211-215] result formulating the relationship between the expected relative squared loss and PCIs. Also a comparison analysis among PCIs is carried out based on various criteria. The result illustrates some advantages of using the index C_pmk over the indices C_pk and C_pm in measuring process capability (yield and loss), since C_pmk always provides a better protection for the customers. Additionally, several extensions and applications to real world problem are also discussed. The paper contains some material presented in the Kotz and Johnson [2002. Process capability indices-a review, 1992-2000. Journal of Quality Technology 34(1), 1-19] survey but from a different perspective. It also discusses the more recent developments during the years 2002-2006.